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An Introduction to Particle Accelerators


... the bending radius,1/ =eB/p, is kept constant during ... Each arc cell has a FODO structure, 106.9 m long. LHC beam transverse size. beta in drift space: ... – PowerPoint PPT presentation

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Title: An Introduction to Particle Accelerators

An Introduction to Particle Accelerators
  • Erik Adli, University of Oslo/CERN
  • 2009

v1.42 - short
LHC FIRST BEAM 10-sep-2008
Part 1
Particle accelerators for HEP
  • LHC the world biggest accelerator, both in
    energy and size (as big as LEP)
  • Grand start-up and perfect functioning at
    injection energy in September 2008
  • First collisions expected in 2009

Particle accelerators for HEP
The next big thing. After LHC, a Linear Collider
of over 30 km length, will probably be needed
Medical applications
  • Therapy
  • The last decades electron accelerators
    (converted to X-ray via a target) are used very
    successfully for cancer therapy)
  • Today's research proton accelerators instead
    (hadron therapy) energy deposition can be
    controlled better, but huge technical challenges
  • Imaging
  • Isotope production for PET scanners

Advantages of proton / ion-therapy
( Slide borrowed from U. Amaldi )
Proton therapy accelerator centre
HIBAC in Chiba
What is all this? Follow the lectures... )
( Slide borrowed from U. Amaldi )
Synchrotron Light Sources
  • the last two decades, enormous increase in the
    use of synchrony radiation, emitted from particle
  • Can produce very intense light (radiation), at a
    wide range of frequencies (visible or not)
  • Useful in a wide range of scientific applications

Thorium - Accelerator Driven Systems
Basic concepts
Part 2
An accelerator
  • Structures in which the particles will move
  • Structures to accelerate the particles
  • Structures to steer the particles

Lorentz equation
  • The two main tasks of an accelerator
  • Increase the particle energy
  • Change the particle direction (follow a given
    trajectory, focusing)
  • Lorentz equation
  • FB ? v ? FB does no work on the particle
  • Only FE can increase the particle energy
  • FE or FB for deflection? v ? c ? Magnetic field
    of 1 T (feasible) same bending power as en
    electric field of 3?108 V/m (NOT feasible)
  • FB is by far the most effective in order to
    change the particle direction

Acceleration techniques DC field
  • The simplest acceleration method DC voltage
  • Energy kick DEqV
  • Can accelerate particles over many gaps
    electrostatic accelerator
  • Problem breakdown voltage at 10MV
  • DC field still used at start of injector chain

Acceleration techniques RF field
  • Oscillating RF (radio-frequency) field
  • Widerøe accelerator, after the pioneering work
    of the Norwegian Rolf Widerøe (brother of the
    aviator Viggo Widerøe)
  • Particle must sees the field only when the field
    is in the accelerating direction
  • Requires the synchronism condition to hold
    Tparticle ½TRF
  • Problem high power loss due to radiation

Acceleration techniques RF cavities
  • Electromagnetic power is stored in a resonant
    volume instead of being radiated
  • RF power feed into cavity, originating from RF
    power generators, like Klystrons
  • RF power oscillating (from magnetic to electric
    energy), at the desired frequency
  • RF cavities requires bunched beams (as opposed to
    coasting beams)
  • particles located in bunches separated in space

From pill-box to real cavities
(from A. Chao)
LHC cavity module
ILC cavity
Why circular accelerators?
  • Technological limit on the electrical field in an
    RF cavity (breakdown)
  • Gives a limited ?E per distance
  • ? Circular accelerators, in order to re-use the
    same RF cavity
  • This requires a bending field FB in order to
    follow a circular trajectory (later slide)

The synchrotron
  • Acceleration is performed by RF cavities
  • (Piecewise) circular motion is ensured by a guide
    field FB
  • FB Bending magnets with a homogenous field
  • In the arc section
  • RF frequency must stay locked to the revolution
    frequency of a particle (later slide)
  • Synchrotrons are used for most HEP experiments
    (LHC, Tevatron, HERA, LEP, SPS, PS) as well as,
    as the name tells, in Synchrotron Light Sources
    (e.g. ESRF)

Digression other accelerator types
  • Cyclotron
  • constant B field
  • constant RF field in the gap increases energy
  • radius increases proportionally to energy
  • limit relativistic energy, RF phase out of synch
  • In some respects simpler than the synchrotron,
  • and often used as medical accelerators
  • Synchro-cyclotron
  • Cyclotron with varying RF phase
  • Betatron
  • Acceleration induced by time-varying magnetic
  • The synchrotron will be the only circular
    accelerator discussed in this course

Digression other accelerator types
  • Linear accelerators for linear colliders
  • - will be covered in lecture about linear
    colliders at CERN

Particle motion
  • We separate the particle motion into
  • longitudinal motion motion tangential to the
    reference trajectory along the accelerator
    structure, us
  • transverse motion degrees of freedom orthogonal
    to the reference trajectory, ux, uy
  • us, ux, uy are unit vector in a moving coordinate
    system, following the particle

Longitudinal dynamicsfor a synchrotron
Part 3
Longitudinal Dynamics degrees of freedom
tangential to the reference trajectory us
tangential to the reference trajectory
RF acceleration
  • We assume a cavity with an oscillating RF-field
  • In this section we neglect the transit-transit
  • we assume a field constant in time while the
    particle passes the cavity
  • Work done on a particle inside cavity

Synchrotron with one cavity
  • The energy kick of a particle, DE, depends on the
    RF phase seen, f
  • We define a synchronous particle, s, which
    always sees the same phase fs passing the cavity
  • ? wRF h wrs ( h harmonic number )
  • E.g. at constant speed, a synchronous particle
    circulating in the synchrotron, assuming no
    losses in accelerator, will always see fs0

Non-synchronous particles
  • A synchronous particle P1 sees a phase fs and get
    a energy kick DEs
  • A particle N1 arriving early with f fs-d will
    get a lower energy kick
  • A particle M1 arriving late with f fsd will get
    a higher energy kick
  • Remember in a synchrotron we have bunches with a
    huge number of particles, which will always have
    a certain energy spread!

Frequency dependence on energy
  • In order to see the effect of a too low/high DE,
    we need to study the relation between the change
    in energy and the change in the revolution
    frequency (h "slip factor")
  • Two effects
  • Higher energy ? higher speed (except
  • Higher energy ? larger orbit Momentum

Momentum compaction
  • Increase in energy/mass will lead to a larger
  • We define the momentum compaction factor as
  • a is a function of the transverse focusing in
    the accelerator, altDxgt / R
  • ? a is a well defined quantity for a given

Phase stability
  • hgt0 velocity increase dominates, fr increases
  • Synchronous particle stable for 0ºltfslt90º
  • A particle N1 arriving early with f fs-d will
    get a lower energy kick, and arrive relatively
    later next pass
  • A particle M1 arriving late with f fsd will get
    a higher energy kick, and arrive relatively
    earlier next pass
  • hlt0 stability for 90ºltfslt180º
  • h0 at the transition energy. When the
    synchrotron reaches this energy, the RF phase
    needs to be switched rapidly from fs to 180-fs

Transverse dynamics
Part 4
Transverse dynamics degrees of freedom
orthogonal to the reference trajectory ux the
horizontal plane uy the vertical plane
Bending field
  • Circular accelerators deflecting forces are
  • Circular accelerators piecewise circular orbits
    with a defined bending radius ?
  • Straight sections are needed for e.g. particle
  • In circular arc sections the magnetic field must
    provide the desired bending radius
  • For a constant particle energy we need a constant
    B field ? dipole magnets with homogenous field
  • In a synchrotron, the bending radius,1/?eB/p, is
    kept constant during acceleration (last section)

The reference trajectory
  • An accelerator is designed around a reference
    trajectory (also called design orbit in circular
  • This is the trajectory an ideal particle will
    follow and consist of
  • a straight line where there is no bending field
  • arc of circle inside the bending field
  • We will in the following talk about transverse
    deviations from this reference trajectory, and
    especially about how to keep these deviations

Bending field dipole magnets
  • Dipole magnets provide uniform field in the
    desired region
  • LHC Dipole magnets design that allows opposite
    and uniform field in both vacuum chambers
  • Bonus effect of dipole magnets geometrical
    focusing in the horizontal plane
  • 1/? normalized dipole strength, strength of
    the magnet

Focusing field
  • reference trajectory typically centre of the
    dipole magnets
  • Problem with geometrical focusing still large
    oscillations and NO focusing in the vertical
    plane ? the smallest disturbance (like
    gravity...) may lead to lost particle
  • Desired a restoring force of the type Fx,y-kx,y
    in order to keep the particles close to the ideal
  • A linear field in both planes can be derived from
    the scalar pot. V(x,y) gxy
  • Equipotential lines at xyVconst
  • B ? magnet iron surface
  • ? Magnet surfaces shaped as hyperbolas gives
    linear field

Focusing field quadrupoles
  • Quadrupole magnets gives linear field in x and y
  • Bx -gy
  • By -gx
  • However, forces are focusing in one plane and
    defocusing in the orthogonal plane
  • Fx -qvgx (focusing)
  • Fy qvgy (defocusing)
  • Opposite focusing/defocusing is achieved by
    rotating the quadrupole 90?
  • Analogy to dipole strength normalized quadrupole

inevitable due to Maxwell
Optics analogy
  • Physical analogy quadrupoles ? optics
  • Focal length of a quadrupole 1/f kl
  • where l is the length of the quadrupole
  • Alternating focusing and defocusing lenses will
    together give total focusing effect in both
    planes (shown later)
  • Alternating Gradient focusing

The Lattice
  • An accelerator is composed of bending magnets,
    focusing magnets and non-linear magnets (later)
  • The ensemble of magnets in the accelerator
    constitutes the accelerator lattice

Example lattice components
Transverse beam size
  • RMS beam size

Beam quality
Conclusion transverse dynamics
  • We have now studied the transverse optics of a
    circular accelerator and we have had a look at
    the optics elements,
  • the dipole for bending
  • the quadrupole for focusing
  • the sextupole for chromaticity correction
  • All optic elements ( more) are needed in a high
    performance accelerator, like the LHC

Synchrotron radiation
Part 5
1) Synchrotron radiation
  • Charged particles undergoing acceleration emit
    electromagnetic radiation
  • Main limitation for circular electron machines
  • RF power consumption becomes too high
  • The main limitation factor for LEP...
  • ...the main reason for building LHC !
  • However, synchrotron radiations is also useful
    (see later slides)

Show RAD2D here
  • (anim)

Characteristic of SR power
Characteristics of SR distribution
  • Electron rest-frame radiation distributed as a
  • Relativist electron Hertz-dipole distribution in
    the electron rest-frame, but transformed into the
    laboratory frame the radiation form a very
    sharply peaked light-cone

Characteristics of SR spectrum
  • Broad spectra (due to short pulses as seen by an
  • But, 50 of power contained within a well defined
    "critical frequency"
  • Summary advantages of Synchrotron Radiation
  • Very high intensity
  • Spectrum that cannot be covered easy with other
  • Critical frequency easily controlled

Typical SR centre
Example European Synchrotron Radiation Facility
(ESRF), Grenoble, France
Accelerator Users
  • Some applications of Synchrotron Radiation
  • material/molecule analysis (UV, X-ray)
  • crystallography
  • archaeology...

Case LHC
LHC injector system
  • LHC is responsible for accelerating protons from
    450 GeV up to 7000 GeV
  • 450 GeV protons injected into LHC from the SPS
  • PS injects into the SPS
  • LINACS injects into the PS
  • The protons are generated by a Duoplasmatron
    Proton Source

LHC layout
  • circumference 26658.9 m
  • 8 interaction points, 4 of which contains
    detectors where the beams intersect
  • 8 straight sections, containing the IPs, around
    530 m long
  • 8 arcs with a regular lattice structure,
    containing 23 arc cells
  • Each arc cell has a FODO structure, 106.9 m long

LHC beam transverse size
beta in drift space b(s) b (s-s)2 / b
LHC cavities
  • Superconducting RF cavities (standing wave, 400
  • Each beam one cryostats with 44 cavities each
  • Located at LHC point 4

LHC main parametersat collision energy
  • Bibliography
  • K. Wille, The Physics of Particle Accelerators,
  • ...and the classic E. D. Courant and H. S.
    Snyder, "Theory of the Alternating-Gradient
    Synchrotron", 1957
  • CAS 1992, Fifth General Accelerator Physics
    Course, Proceedings, 7-18 September 1992
  • LHC Design Report online
  • Other references
  • USPAS resource site, A. Chao, USPAS january 2007
  • CAS 2005, Proceedings (in-print), J. Le Duff, B,
    Holzer et al.
  • O. Brüning CERN student summer lectures
  • N. Pichoff Transverse Beam Dynamics in
    Accelerators, JUAS January 2004
  • U. Amaldi, presentation on Hadron therapy at CERN
  • Several figures in this presentation have been
    borrowed from the above references, thanks to all!